Once unlocked, the double reputation gains should affect your characters across servers much the same way that account-wide pets are accessible to all characters on the account. All your Horde characters will share the same reputation gain bonus.

While we're talking about this, I've been wondering why while I have 169 mounts on Alliance side, I only have 98 on Horde side. I created a Horde character (now level 67) and he has access only to mounts that are available to both factions. None of the Horde faction mounts are available. I would have thought that the equivalent mounts would be available just like when you faction change. I have the old school ride achievement, but no mount to show for it on horde side.

I don't see your account as having any Horde specific mounts. Have you purchased any Horde mounts?